A077320 Triangle in which n-th row contains n smallest multiples of the n-th prime.

2, 3, 6, 5, 10, 15, 7, 14, 21, 28, 11, 22, 33, 44, 55, 13, 26, 39, 52, 65, 78, 17, 34, 51, 68, 85, 102, 119, 19, 38, 57, 76, 95, 114, 133, 152, 23, 46, 69, 92, 115, 138, 161, 184, 207, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290

Offset: 1

Author

Amarnath Murthy, Nov 04 2002

Keywords

• nonn
• tabl
• easy

Comments

0. A000040 (primes) gives initial terms of rows.

1. A033286 contains the final terms of rows.

2. Sum of the n-th row = prime(n)*A000217(n), by definition.

3. a(A000217(n) + 1) = prime(n+1), by definition.

Examples

			From _Bruno Berselli_, Sep 05 2017: (Start)
Triangle begins:
   2;
   3, 6;
   5, 10,  15;
   7, 14,  21,  28;
  11, 22,  33,  44,  55;
  13, 26,  39,  52,  65,  78;
  17, 34,  51,  68,  85, 102, 119;
  19, 38,  57,  76,  95, 114, 133, 152;
  23, 46,  69,  92, 115, 138, 161, 184, 207;
  29, 58,  87, 116, 145, 174, 203, 232, 261, 290;
  31, 62,  93, 124, 155, 186, 217, 248, 279, 310, 341;
  37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 407, 444;
  41, 82, 123, 164, 205, 246, 287, 328, 369, 410, 451, 492, 533;
  43, 86, 129, 172, 215, 258, 301, 344, 387, 430, 473, 516, 559, 602, etc.
(End)
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8128

Crossrefs

Cf. A000040, A000217, A033286.

Row sums give A196421. - Omar E. Pol, Mar 12 2012

Programs

Mathematica

Table[Prime[n]*Range[n], {n, 10}] // Flatten (* Ivan Neretin, May 02 2019 *)

Formula

T(n,k) = k*prime(n) with 1 <= k <= n. - Bruno Berselli, Sep 05 2017